The present invention relates to a method of monitoring torsional vibration produced in a rotating shaft system for use in a device such as a turbine generator which comprises the steps of measuring torsional vibrations produced in the rotating shaft system at a small number of certain positions on the shaft system at which the measurements of the torsional vibrations are possible, linearly decomposing the measured torsional vibrations and estimating torsional vibrations at other arbitrary positions on the rotating shaft system from the estimations, and to an apparatus for performing the same.